Homes on the Falinge estate in Rochdale, north-west England, one of the country’s most deprived areas.
Photograph: Christopher Furlong/Getty Images

Life had already been a struggle for months when the letter arrived from the Department for Work and Pensions last week telling Alana and Mark they would be benefit capped. From Monday, it said, the amount they would receive in housing benefit support – which is already £260 a month less than their actual rent – would be cut by £50 a week.

It was a none-too-subtle signal for Alana that life was about to get several degrees harder. “Saving an extra £200 a month is going to be impossible. We can’t cover the outgoings as it is. No amount of budgeting can save that sort of money. There’s only so much you can save on buying basic label baked beans.”

Both Alana and Mark, the parents of two small children, have lost good jobs through redundancy in the past year. They have scraped by since on her maternity allowance, borrowed cash from family and friends, and sold furniture. The cap in effect now provides them with stark alternatives: either one of them gets work (thus exempting them from the cap), or they fall rapidly into rent arrears and eviction.

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Alana and Mark are not alone in being handed such a brutal choice. Estimates vary, but between 88,000 and 116,000 struggling UK households have received similar benefit cap letters from the DWP in recent weeks. On average they will lose £60 a week, though in some cases it could be as high as £150 a week. For many there will be no choice: they cannot work or are unable to find it, and as a result face hunger, impoverishment and homelessness.

The benefit cap was originally introduced by the coalition government as a device to supposedly “restore fairness” to the benefit system by limiting total household benefit income to no more than the average working family earnings of £26,000 a year. Emboldened by the cap’s apparent popularity with the public, the Conservatives changed the law earlier this year to lower it to £20,000 (£23,000 in London). The new cap will be rolled out across the UK between now and February, affecting about four times as many households as its predecessor.

Formal evaluations of the cap suggest it has only the mildest of positive effects on employment. The Institute for Fiscal Studies, in a study note published on Sunday, estimates that only 5% of the 80,000 households hit by the first cap moved into employment as a result. A study published in the summer by Oxford city council in partnership, ironically, with the DWP, found that cutting people’s benefits reduced their chances of moving into work, because dealing with the additional pressures of poverty eroded their capacity for job seeking. Other studies have suggested that most of those who have moved off the cap into a job were close to working anyway, leaving those further from the job market deeper in debt and despair.

Many of those who have been unable to escape the cap have simply been unable to work – and have only managed to pay the rent by cutting back drastically on living costs or going into debt. Local authorities are increasingly worried that the cap, in its bigger and more punitive form, will trigger a surge in rent arrears, ill health and homelessness.

The secretary of state for work and pensions, Damian Green, said: “By making sure that those people who are out of work are faced with the same choices as those who are in work, the benefit cap has been a real success.

“By lowering the cap today, we are ensuring the values of this government continue to chime with those of ordinary working people and delivering on our commitment to make sure work pays more than welfare”.

Meanwhile, Alana notes that her private landlord has just served a notice saying the family’s rent is going up by £25 a month. As she speculates on the increasingly limited ways in which she might cope with the cap, she recalls the offer made by her NHS health visitor on a recent visit: if she did find herself struggling to feed the baby, a voucher for the food bank could be made available.

They now face an anxious wait: Mark has been promised a minimum wage job in the care sector. This would rescue them from the cap but no start date has been set. The longer the delay, the more debt, stress and rent arrears will build, and the prospect of eviction will be more likely. “If there’s a choice between paying the rent and feeding myself and the kids, I’ll feed my kids,” said Alana.

Alana and Mark are almost certainly not who ministers and tabloids have in mind when they hail the supposed bracingly motivational qualities of benefit cuts, or stir rancour against “scroungers”. They moved out to their comfortably middle-English market town in the east of the country two years ago to find cheaper rents and a nice place to bring up children. Then redundancy disaster struck. In a sense they are a classic example of the “just managing” family the prime minister, Theresa May, says she wants to help, though the benefit cap instead threatens to rapidly unpick the last fraying strands of the social security safety net keeping them from destitution.

“They are out of touch with reality,” said Alana. “They expect people to live on a tiny amount of money. It’s not like benefits are generous. It’s completely misleading, this idea that people live comfortably on benefits, a fallacy.”

• Names have been changed

• This article was amended on 9 November 2016. An earlier version said the benefit cap was introduced to limit total household benefit income to no more than the average working family income of £26,000 a year. The cap was set at the average working family earnings, not total income (earnings plus benefits).